Gender categories refer here to the assignment of a gender to a noun which may be marked morphologically in several ways. It has nothing to do with expressing natural gender.
Masculine, feminine, and neuter are characteristics of Indo-European languages. Many of them have lost the neuter like Romance languages (except Romanian and Asturian), Celtic languages, Baltic languages, and most Indo-Aryan languages.
Some, like Dutch, Danish and Swedish have merged the masculine and the feminine into a common gender, making thus a distinction more similar to animate and inanimate.
Genderless languages are the most common: Turkic, Tungusic, Sino-Tibetan, Mongolic, Koreanic, Japonic, Kartvelian, Pontic, Uralic, Austronesian, Austroasiatic, Tai-Kadai, Pama-Nyungan, and most Australian languages, Tupi-Gê-Carib, Arawan, Arawak, Na-Dene, Eskimo-Aleut, and many others in Papua and the Americas. English and Afrikaans lost all gender marking except in pronouns (he, she, it, for example).
Several diverse classes occur in most Niger-Congo languages, some Caspian/Northeast Caucasian languages, some Khoisan languages, Jarawa and Ongan (from the Andaman Islands), and some aboriginal Australian languages. They may contain animal genders, vegetal genders, genders for rocks, and many other categories.
Animate and inanimate gender is common in some Amerindian families such as Algic, Uto-Aztecan, Quechuan, Aymara, Mapudungun, Iroquoian, Siouan.
Burushaski and Zande have four genders, masc., fem., animate and inanimate, and some like Polish, Czech, or the Dravidian Languages have a hierarchy of animacy and gender.
Read more: Linguistic maps. Linguistic maps featuring several grammatical and phonological features, created by Rodrigo Pereira, a linguist, and conlanger.